Testing SDLCQ in 2+1 dimensions

TL;DR

This paper tests the SDLCQ regularization's ability to preserve supersymmetry in 2+1 dimensions by analyzing the spectrum of supersymmetric Yang-Mills theory on a compactified spacetime, demonstrating convergence and stability of bound state masses.

Contribution

It extends the application of SDLCQ to higher dimensions, specifically 2+1, and provides numerical evidence of its effectiveness in preserving supersymmetry and analyzing the spectrum.

Findings

Masses converge rapidly with increasing resolutions.

Stable spectrum observed at strong coupling.

Unphysical states decouple at large transverse resolution.

Abstract

The SDLCQ regularization is known to explicitly preserve supersymmetry in 1+1 dimensions. To test this property in higher dimensions, we consider supersymmetric Yang-Mills theory on R x S^1 x S^1. In particular, we choose one of the compact directions to be light-like and another to be space-like. This theory is totally finite, and thus we can solve for bound state wave functions and masses numerically without renormalizing. We present the masses as functions of the longitudinal and transverse resolutions and show that the masses converge rapidly in both resolutions. We study the behavior of the spectrum as a function of the coupling and find that at strong coupling there is a stable, well-defined spectrum which we present. We discuss also the massless spectrum and find several unphysical states that decouple at large transverse resolution.